Abstract
We study 4D $$ \mathcal{N} $$ = 2 superconformal theories that arise from the compactification of 6D $$ \mathcal{N} $$ = (2, 0) theories of type A 2N −1 on a Riemann surface C, in the presence of punctures twisted by a ℤ2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A 3, and provide tables of properties of twisted defects up through A 9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.
Highlights
Introduction and summaryConsiderable progress has been made recently in the program of understanding the 4D theories that arise from the compactification of 6D N = (2, 0) theories on a Riemann surface, C, possibly in the presence of codimension-two defects of the (2,0) theories, which correspond to punctures on C [1,2,3,4,5].1 Much of the richness of the construction stems from the variety of available defects
We study 4D N = 2 superconformal theories that arise from the compactification of 6D N = (2, 0) theories of type A2N−1 on a Riemann surface C, in the presence of punctures twisted by a Z2 outer automorphism
We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A3, and provide tables of properties of twisted defects up through A9
Summary
(For example, [62, 34, 2] is a C-partition, but [52, 3, 1] is not.) a twisted puncture in the A2N−1 series is labeled by a B-partition ρ of 2N + 1, but its Higgs-field boundary condition is given by a C-partition ρ′ of 2N. In [6], ρ′ was called the Hitchin pole of the puncture labeled by the Nahm pole ρ. ρ′ is given by the C-collapse of the reduction of the transpose of ρ (a 2N + 1 partition) to a 2N partition; see section 2.2 and section 3.4.4 of [6]
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